Question

Prove that sinx+sin3x+sin5x+sin7x/cosx+cos3x+cos5x+cos7x=tan4x

Answer 1

Step-by-step explanation:

USE THE FORMULA..

sin c+sin d = 2sin(c+d)/2 × cos(c-d)/2

cos c+ cos d = 2cos(c+d)/2 × cos(c-d)/2

Answer 2

Answer with Step-by-step explanation:

LHS :

$\frac{sinx+sin3x+sin5x+sin7x}{cosx+cos3x+cos5x+cos7x}$

$\frac{(sinx+sin3x)+(sin5x+sin7x)}{(cosx+cos3x)+(cos5x+cos7x)}$

We know that

$sinx+siny=2sin\frac{x+y}{2}cos\frac{x-y}{2}$

$cosx+cosy=2cos\frac{x+y}{2}cos\frac{x-y}{2}$

Using the formula

$\frac{2sin2xcosx+2sin6xcosx}{2cos2xcosx+2cos6xcosx}$

$\frac{2cosx(sin2x+sin6x}{2cosx(cos2x+cos6x)}$

$\frac{sin2x+sin6x}{cos2x+cos6x}$

$\frac{2sin4xcos2x}{2cos4xcos2x}$

$\frac{sin4x}{cos4x}$

$tan4x$=RHS

Using the formula

$tanx=\frac{sinx}{cosx}$

Hence, proved.

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https://brainly.in/question/1023077:Answered by Abhi